Radar imaging system and method using gradient magnitude second moment spatial variance detection

ABSTRACT

A detection system and method. The inventive system includes an arrangement for receiving a frame of image data; an arrangement for performing a rate of change of variance calculation with respect to at least one pixel in said frame of image data; and an arrangement for comparing said calculated rate of change of variance with a predetermined threshold to provide output data. In the illustrative embodiment, the frame of image data includes a range/Doppler matrix of N down range samples and M cross range samples. In this embodiment, the arrangement for performing a rate of change of variance calculation includes an arrangement for calculating a rate of change of variance over an N×M window within the range/Doppler matrix. The arrangement for performing a rate of change of variance calculation includes an arrangement for identifying a change in a standard deviation of a small, localized sampling of cells. In accordance with the invention, the arrangement for performing a rate of change of variance calculation outputs a rate of change of variance pixel map.

REFERENCE TO COPENDING APPLICATIONS

This application claims the benefit of U.S. Provisional Application No.60/854,861, filed Oct. 26, 2006, the disclosure of which is herebyincorporated by reference. In addition, copending patent applicationsentitled RADAR IMAGING SYSTEM AND METHOD USING SECOND MOMENT SPATIALVARIANCE and RADAR IMAGING SYSTEM AND METHOD USING DIRECTIONAL GRADIENTMAGNITUDE SECOND MOMENT SPATIAL VARIANCE DETECTION, filed by ______ D.P. Bruyere et al., Ser. Nos. ______ and (Atty. Docket Nos. PD 06W129 andPD 06W137) involve second moment detection and directional gradientsecond moment detection, respectively, the teachings of which are herebyincorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to radar systems and associated methods.More specifically, the present invention relates to systems and methodsfor improving radar image quality.

2. Description of the Related Art

Synthetic Aperture Radar (SAR) uses a side looking radar aperture on amoving platform to provide high-resolution imagery over a broad area.The concept usually employs airborne radar that collects data whileflying some distance, and then processes the data coherently as if itcame from a physically long antenna (See Introduction to Airborne Radarby G. W. Stimson, published 1998 by Scitech Pub Inc, pp. 527-549.)

This synthetically long antenna aperture provides superior imageresolution over that of the actual antenna and overcomes the weatherdependent nature of all optical remote-sensing systems. While theability of SAR radars to produce better and better imagery advances, theability of those same radars to autonomously distinguish stationaryground vehicles from background clutter remains difficult.

Template based methods use previously collected images from knownvehicles to identify targets within a scene. (See “The AutomaticTarget-Recognition System in SAIP”, by L. M. Novak, et al., LincolnLaboratory Journal, vol. 10, no. 2, pp 187-203, 1997 and “An efficientmulti-target SAR ATR Algorithm”, by L. M. Novak, et al., published bythe Massachusetts Institute of Technology/Lincoln Laboratory, Lexington,Mass.)

The process of template based target identification begins with a simplelocalized constant false alarm rate (CFAR) detection test to remove anyobjects that are not locally bright, then a discrimination layer isapplied that removes any non-target like objects. These two layers ofprocessing are performed before the template processing is applied,since the template based processing can be easily overwhelmed with ahigh false alarm rate.

Another problem of template based target identification is that itsperformance is based on prior knowledge of the target. The total numberof different target types that need to be identified also affectsperformance. One drawback of template based target detection methods isthat small variations in target configurations can reduce theeffectiveness of the templates.

Also, since a SAR image contains many small scatters whose physical sizeis on the order of the radar's wavelength, constructive and destructiveinterference of the complex returns produces phenomena called speckle,which reduces image quality and decreases probability of targetdetection. Smoothing and spatial filtering techniques can reduce speckleand help increase the probability of detection. (See “Application ofangular correlation function of clutter scattering and correlationimaging in target detection”, by G. Zhang, L. Tsang, IEEE Transactionson Geoscience and Remote Sensing, Volume 36, Issue 5, Part 1, pp.1485-1493, September 1998.) However, these approaches remain inadequatefor current more demanding applications.

Hence, a need remains in the art for an improved radar system or methodfor imaging a target that addresses problems associated with speckle.

SUMMARY OF THE INVENTION

The need in the art is addressed by the detection system and method ofthe present invention. The inventive detection system includes means forreceiving a frame of image data; means for performing a rate of changeof variance calculation with respect to at least one pixel in the frameof image data; and means for comparing the calculated rate of change ofvariance with a predetermined threshold to provide output data. In theillustrative embodiment, the frame of image data includes arange/Doppler matrix of N down range samples and M cross range samples.In this embodiment, the means for performing a rate of change ofvariance calculation includes means for calculating a rate of change ofvariance over an N×M window within the range/Doppler matrix. The meansfor performing a rate of change of variance calculation includes meansfor identifying a change in a standard deviation of a small, localizedsampling of cells. The means for performing a rate of change of variancecalculation outputs a rate of change of variance pixel map.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an illustrative embodiment of an imagingradar system implemented in accordance with the present teachings.

FIG. 2 is a flow diagram of an illustrative embodiment of a method fordetection processing in accordance with the present teachings.

FIG. 3 is a flow diagram of an illustrative embodiment of a method forgradient magnitude second moment detection processing in accordance withthe teachings of the present invention.

FIG. 4 is a diagram that illustrates the Roberts operation for taking atwo-dimensional derivative of variance in accordance with anillustrative embodiment of the present teachings.

FIG. 5 is a flow diagram in more detail of an illustrative embodiment ofa method for gradient magnitude second moment detection processing inaccordance with the teachings of the present invention.

DESCRIPTION OF THE INVENTION

Illustrative embodiments and exemplary applications will now bedescribed with reference to the accompanying drawings to disclose theadvantageous teachings of the present invention.

While the present invention is described herein with reference toillustrative embodiments for particular applications, it should beunderstood that the invention is not limited thereto. Those havingordinary skill in the art and access to the teachings provided hereinwill recognize additional modifications, applications, and embodimentswithin the scope thereof and additional fields in which the presentinvention would be of significant utility.

The present invention exploits a recognition that for complex targetsviewed from airborne radar, a high degree of scene variance can providebetter detection of a fluctuating target than amplitude based detectionmethods. This alternative method of distinguishing targets frombackground is presented that can be used instead of, or in conjunctionwith the template based processing techniques previously discussed.

Most scene based detection methods use amplitude as a means ofidentifying a target within the scene. Man-made targets generally have ahigh radar cross-section (RCS) that can make them brighter than thesurrounding clutter. Factors that contribute to RCS include the physicalsize of target, the number of reflective surfaces, angles of thereflective surfaces, and the reflective properties of the material fromwhich the target is made. However, even if a target has a large RCS,there is no guarantee that reflective characteristics alone willdistinguish the target from other bright objects within the scene. Somenatural backgrounds, such as snow that has been partially melted andrefrozen, are highly reflective and can generate large radar returnsthat easily overshadow the returns from most man-made target types. SARimages of man-made targets have inherent characteristics that can beexploited to enhance detection of these targets. The multi-facetted,sometimes specular surfaces that land or air vehicles have, as do somebuildings, help to distinguish them from normal background features suchas grassy fields, roads, and trees.

Most man-made vehicles are made up of many small dihedral cornerreflectors. The constructive and destructive nature of these targetreturns manifests itself in a SAR image as a high variation of signalamplitudes within a very localized area. This invention exploits thefact that these highly reflective, multifaceted features buildconstructively and fade in localized regions within the scene. Theserapidly changing returns manifest themselves as a high degree of localscene variance, which can be measured by calculating the variance of asmall group of pixels within a SAR scene. By using local scene varianceas a distinguishing factor, enhanced detection of these target typesover a variety of background types and conditions may be achieved. Theassociated image created from the localized variance calculations isreferred to as either a variance or standard deviation image.

The present invention exploits inherent characteristics associated withmost target types to improve detection within SAR images. The presentinvention involves second moment detection. Copending patentapplications entitled RADAR IMAGING SYSTEM AND METHOD USING SECONDMOMENT SPATIAL VARIANCE and RADAR IMAGING SYSTEM AND METHOD USINGDIRECTIONAL GRADIENT MAGNITUDE SECOND MOMENT SPATIAL VARIANCE DETECTION,filed by ______ D. P. Bruyere et al., Ser. Nos. ______ and (Atty. DocketNos. PD 06W129 and PD 06W137) involve second moment detection anddirectional gradient second moment detection, respectively, theteachings of which are hereby incorporated herein by reference.

The invention operates on complex SAR images, where each pixelrepresents the signal amplitude received at a particular down range andcross range location relative to the aircraft. Nonetheless, those ofordinary skill in the art will appreciate that the present invention isnot limited thereto. The present teachings may be applied to imagesgenerated by other means without departing from the scope thereof.

In accordance with the present teachings, a second moment image isderived from the input (e.g. SAR) image and a derivative image iscreated with respect to the second moment image. As discussed more fullybelow, each pixel of the second moment image represents the localstandard deviation of pixel amplitudes from a small region in theoriginal SAR image. A bright pixel in the second moment image representsan area with a high degree of local scene variance within the originalscene. Alternatively, dark pixels represent a very low degree of localvariance.

Second Moment Generalized Likelihood Ratio Test

To develop a generalized likelihood ratio test, assume that thedistribution of the scene data is complex Gaussian whether there is atarget present or not. The mean and standard deviations of therespective distributions are unknown and assumed to be different undereach hypothesis. By collecting a small sample of range Doppler cellsabout the cell under test, we assume that we can determine whether thestatistics implied by the sample cells indicate that the samples arefrom target cells or background cells. This controls the size of thesample that we select, since it has to be smaller than the target ofinterest.

The likelihood ratio test thus begins with a small matrix of pixels, X,that is made up of N down range samples by M cross range samples. Thispresumes a square sample area for convenience of the derivation. We willassume measurements to be independent from one pixel to the next, so thejoint probability distribution under the target present is the productof the probability density functions (pdf's) associated with eachindividual measurement. For a small region of SAR pixels under test thetarget present and target absent hypothesis probability distributionsare:

$\begin{matrix}{{p\left( {X;\frac{\theta_{1}}{H_{1}}} \right)} = {{\prod\limits_{n = {- \frac{N}{2}}}^{\frac{N}{2}}\; {\prod\limits_{m = {- \frac{M}{2}}}^{\frac{M}{2}}{\frac{1}{\left( {\pi\sigma}_{H\; 1}^{2} \right)}^{(\frac{{{{- {x{\lbrack{n,m}\rbrack}}} - A_{1}})}^{H}{({{x{\lbrack{n,m}\rbrack}} - A_{1}})}}{\sigma_{H\; 1}^{2}})}}}} = {\frac{1}{\left( {\pi\sigma}_{H\; 1}^{2} \right)^{NM}}{\exp\left( \frac{- {\sum\limits_{n = {- \frac{N}{2}}}^{\frac{N}{2}}\; {\sum\limits_{m = {- \frac{M}{2}}}^{\frac{M}{2}}\; {\left( {{x\left\lbrack {n,m} \right\rbrack} - A_{1}} \right)^{H}\left( {{x\left\lbrack {n,m} \right\rbrack} - A_{1}} \right)}}}}{\sigma_{H\; 1}^{2}} \right)}}}} & (0.1) \\{and} & \; \\{{p\left( {X;\frac{\theta_{0}}{H_{0}}} \right)} = {{\prod\limits_{n = {- \frac{N}{2}}}^{\frac{N}{2}}\; {\prod\limits_{m = {- \frac{M}{2}}}^{\frac{M}{2}}{\frac{1}{\left( {\pi\sigma}_{H\; 0}^{2} \right)}^{(\frac{{{{- {x{\lbrack{n,m}\rbrack}}} - A_{0}})}^{H}{({{x{\lbrack{n,m}\rbrack}} - A_{0}})}}{\sigma_{H\; 0}^{2}})}}}} = {\frac{1}{\left( {\pi\sigma}_{H\; 0}^{2} \right)^{NM}}{\exp\left( \frac{- {\sum\limits_{n = {- \frac{N}{2}}}^{\frac{N}{2}}\; {\sum\limits_{m = {- \frac{M}{2}}}^{\frac{M}{2}}\; {\left( {{x\left\lbrack {n,m} \right\rbrack} - A_{0}} \right)^{H}\left( {{x\left\lbrack {n,m} \right\rbrack} - A_{0}} \right)}}}}{\sigma_{H\; 0}^{2}} \right)}}}} & (0.2)\end{matrix}$

respectively, where x[n,m] is an individual pixel that is located at ndown range and m cross range. The probability distribution functions areparameterized by unknown variables

$\begin{matrix}\begin{matrix}\left. \theta_{1}\Rightarrow\begin{bmatrix}A_{1} \\\sigma_{H\; 1}^{2}\end{bmatrix} \right. \\\left. \theta_{0}\Rightarrow\begin{bmatrix}A_{0} \\\sigma_{H\; 0}^{2}\end{bmatrix} \right.\end{matrix} & (0.3)\end{matrix}$

where A₁ and σ_(H1) are the mean and the standard deviation of thetarget present hypothesis, and A₀ and σ_(H0) are the mean and thestandard deviation of the target present hypothesis. Given this, thelikelihood ratio test begins as:

$\begin{matrix}{\Lambda = {\frac{p\left( {X;\frac{\theta_{1}}{H_{1}}} \right)}{p\left( {X;\frac{\theta_{0}}{H_{0}}} \right)} = {\frac{\frac{1}{\left( {\pi\sigma}_{H\; 1}^{2} \right)^{NM}}{\exp\left( \frac{\; \begin{matrix}{- {\sum\limits_{n = {- \frac{N}{2}}}^{\frac{N}{2}}\; \sum\limits_{m = {- \frac{M}{2}}}^{\frac{M}{2}}}} \\\begin{matrix}\left( {{x\left\lbrack {n,m} \right\rbrack} - A_{1}} \right)^{H} \\\left( {{x\left\lbrack {n,m} \right\rbrack} - A_{1}} \right)\end{matrix}\end{matrix}}{\sigma_{H\; 1}^{2}} \right)}}{\frac{1}{\left( {\pi\sigma}_{H\; 0}^{2} \right)^{NM}}{\exp\left( \frac{\; \begin{matrix}{- {\sum\limits_{n = {- \frac{N}{2}}}^{\frac{N}{2}}\; \sum\limits_{m = {- \frac{M}{2}}}^{\frac{M}{2}}}} \\\begin{matrix}\left( {{x\left\lbrack {n,m} \right\rbrack} - A_{0}} \right)^{H} \\\left( {{x\left\lbrack {n,m} \right\rbrack} - A_{0}} \right)\end{matrix}\end{matrix}}{\sigma_{H\; 0}^{2}} \right)}}{\begin{matrix}{{> {Threshold}}->{H\; 1}} \\{{< {Threshold}}->{H\; 0}}\end{matrix}.}}}} & (0.4)\end{matrix}$

In order to solve for the unknown means and standard deviations, we mustmaximize the target present hypothesis (0.1) with respect to theunknowns in (0.3). We start by maximizing the expression with respect tothe unknown amplitude: A₁. Taking the natural log of both sides of theequation, we get an expression that is easier to work with:

$\begin{matrix}{{\ln \left\lbrack {p\left( {X;\frac{\theta_{1}}{H_{1}}} \right)} \right\rbrack} = {{\ln \left( \frac{1}{\left( {\pi\sigma}_{H\; 1}^{2} \right)^{NM}} \right)} - \frac{\sum\limits_{n = {- \frac{N}{2}}}^{\frac{N}{2}}\; {\sum\limits_{m = {- \frac{M}{2}}}^{\frac{M}{2}}\; \begin{matrix}\left( {{x\left\lbrack {n,m} \right\rbrack} - A_{1}} \right)^{H} \\\left( {{x\left\lbrack {n,m} \right\rbrack} - A_{1}} \right)\end{matrix}}}{\sigma_{H\; 1}^{2}}}} & (0.5)\end{matrix}$

Taking the derivative of (0.5) with respect to A₁ gives us:

$\begin{matrix}\begin{matrix}{\frac{\partial{\ln \left\lbrack {p\left( {X;\frac{\theta_{1}}{H_{1}}} \right)} \right\rbrack}}{\partial A_{1}} = {\frac{\partial}{\partial A_{1}}\left\lbrack {{\ln \left( \frac{1}{\left( {\pi\sigma}_{H\; 1}^{2} \right)^{NM}} \right)} - \frac{\; \begin{matrix}{\sum\limits_{n = {- \frac{N}{2}}}^{\frac{N}{2}}\; \sum\limits_{m = {- \frac{M}{2}}}^{\frac{M}{2}}} \\\begin{matrix}\left( {{x\left\lbrack {n,m} \right\rbrack} - A_{1}} \right)^{H} \\\left( {{x\left\lbrack {n,m} \right\rbrack} - A_{1}} \right)\end{matrix}\end{matrix}}{\sigma_{H\; 1}^{2}}} \right\rbrack}} \\{= {2{\frac{{\sum\limits_{n = {- \frac{N}{2}}}^{\frac{N}{2}}\; {\sum\limits_{m = {- \frac{M}{2}}}^{\frac{M}{2}}\left( {{x\left\lbrack {n,m} \right\rbrack} - A_{1}} \right)}}\;}{\sigma_{H\; 1}^{2}}.}}}\end{matrix} & (0.6)\end{matrix}$

Setting this expression equal to zero and solving for the unknown meanvalue for the target present hypothesis gives us the maximum likelihoodestimate (MLE):

$\begin{matrix}{{\hat{A}}_{1} = {\frac{1}{NM}{\sum\limits_{n = {- \frac{N}{2}}}^{\frac{N}{2}}\; {\sum\limits_{m = {- \frac{M}{2}}}^{\frac{M}{2}}\left( {x\left\lbrack {n,m} \right\rbrack} \right)}}}} & (0.7)\end{matrix}$

We can take a similar approach to obtain a maximum likelihood estimateof the unknown standard deviation. Taking the derivative of the log withrespect to σ_(H1) ² gives us the following expression:

$\begin{matrix}\begin{matrix}{\frac{\partial{\ln \left\lbrack {p\left( {X;\frac{\theta_{1}}{H_{1}}} \right)} \right\rbrack}}{\partial\sigma_{H\; 1}^{2}} = {\frac{\partial}{\partial\sigma_{H\; 1}^{2}}\left\lbrack {{\ln \left( \frac{1}{\left( {\pi\sigma}_{H\; 1}^{2} \right)^{NM}} \right)} - \frac{\; \begin{matrix}{\sum\limits_{n = {- \frac{N}{2}}}^{\frac{N}{2}}\; \sum\limits_{m = {- \frac{M}{2}}}^{\frac{M}{2}}} \\\begin{matrix}\left( {{x\left\lbrack {n,m} \right\rbrack} - A_{1}} \right)^{H} \\\left( {{x\left\lbrack {n,m} \right\rbrack} - A_{1}} \right)\end{matrix}\end{matrix}}{\sigma_{H\; 1}^{2}}} \right\rbrack}} \\{= {{- \frac{NM}{\left( \sigma_{H\; 1}^{2} \right)}} + {\frac{\sum\limits_{n = {- \frac{N}{2}}}^{\frac{N}{2}}\; {\sum\limits_{m = {- \frac{M}{2}}}^{\frac{M}{2}}\begin{matrix}\left( {{x\left\lbrack {n,m} \right\rbrack} - A_{1}} \right)^{H} \\\left( {{x\left\lbrack {n,m} \right\rbrack} - A_{1}} \right)\end{matrix}}}{\sigma_{H\; 1}^{4}}.}}}\end{matrix} & (0.8)\end{matrix}$

Since we have concluded that Â₁ is the MLE for the unknown targetpresent hypothesis mean, we can substitute it in for A₁ and set theexpression equal to zero to solve for the unknown variance term:

$\begin{matrix}{{\hat{\sigma}}_{H\; 1}^{2} = {\frac{1}{NM}{\sum\limits_{n = {- \frac{N}{2}}}^{\frac{N}{2}}\; {\sum\limits_{m = {- \frac{M}{2}}}^{\frac{M}{2}}{\left( {{x\left\lbrack {n,m} \right\rbrack} - {\hat{A}}_{1}} \right)^{H}{\left( {{x\left\lbrack {n,m} \right\rbrack} - {\hat{A}}_{1}} \right).}}}}}} & (0.9)\end{matrix}$

Understanding that we have similar unknowns under the target absenthypothesis, represented in (0.3), we can proceed in a similar manner tofind their respective MLE's starting with the H₀ probability densityfunction in (0.2) and get similar results for the target absenthypothesis:

$\begin{matrix}{{{\hat{A}}_{0} = {\frac{1}{NM}{\sum\limits_{n = {- \frac{N}{2}}}^{\frac{N}{2}}\; {\sum\limits_{m = {- \frac{M}{2}}}^{\frac{M}{2}}\left( {x\left\lbrack {n,m} \right\rbrack} \right)}}}}{{\hat{\sigma}}_{H\; 0}^{2} = {\frac{1}{NM}{\sum\limits_{n = {- \frac{N}{2}}}^{\frac{N}{2}}\; {\sum\limits_{m = {- \frac{M}{2}}}^{\frac{M}{2}}{\left( {{x\left\lbrack {n,m} \right\rbrack} - {\hat{A}}_{0}} \right)^{H}\left( {{x\left\lbrack {n,m} \right\rbrack} - {\hat{A}}_{0}} \right)}}}}}} & (0.10)\end{matrix}$

Substituting all of the maximum likelihood estimates in for theirunknown counterparts and simplifying, we get an expression for thegeneralized likelihood ratio test for a synthetic aperture scene:

$\begin{matrix}{{{GLRT} = {\frac{p\left( {X;\frac{\theta_{1}}{H_{1}}} \right)}{p\left( {X;\frac{\theta_{0}}{H_{0}}} \right)} = \frac{\frac{1}{\left( {2\pi {\hat{\sigma}}_{H\; 1}^{2}} \right)^{\frac{NM}{2}}}{\exp\left( \frac{\; \begin{matrix}{- {\sum\limits_{n = {- \frac{N}{2}}}^{\frac{N}{2}}\; \sum\limits_{m = {- \frac{M}{2}}}^{\frac{M}{2}}}} \\\begin{matrix}\left( {{x\left\lbrack {n,m} \right\rbrack} - {\hat{A}}_{1}} \right)^{H} \\\left( {{x\left\lbrack {n,m} \right\rbrack} - {\hat{A}}_{1}} \right)\end{matrix}\end{matrix}}{2{\hat{\sigma}}_{H\; 1}^{2}} \right)}}{\frac{1}{\left( {2\pi {\hat{\sigma}}_{H\; 0}^{2}} \right)^{\frac{NM}{2}}}{\exp\left( \frac{\; \begin{matrix}{- {\sum\limits_{n = {- \frac{N}{2}}}^{\frac{N}{2}}\; \sum\limits_{m = {- \frac{M}{2}}}^{\frac{M}{2}}}} \\\begin{matrix}\left( {{x\left\lbrack {n,m} \right\rbrack} - {\hat{A}}_{0}} \right)^{H} \\\left( {{x\left\lbrack {n,m} \right\rbrack} - {\hat{A}}_{0}} \right)\end{matrix}\end{matrix}}{2{\hat{\sigma}}_{H\; 0}^{2}} \right)}}}}{{GLRT} = {\frac{\frac{1}{\left( {2\pi {\hat{\sigma}}_{H\; 1}^{2}} \right)^{\frac{NM}{2}}}}{\frac{1}{\left( {2\pi {\hat{\sigma}}_{H\; 0}^{2}} \right)^{\frac{NM}{2}}}} = {\frac{\left( {2\pi {\hat{\sigma}}_{H\; 0}^{2}} \right)^{\frac{NM}{2}}}{\left( {2\pi {\hat{\sigma}}_{H\; 1}^{2}} \right)^{\frac{NM}{2}}} = {\left( \frac{{\hat{\sigma}}_{H\; 0}^{2}}{{\hat{\sigma}}_{H\; 1}^{2}} \right)^{\frac{NM}{2}}.}}}}} & (0.11)\end{matrix}$

The most significant factor of the resultant expression indicates thatwe can set a threshold that depends strictly on the variance of thelocal statistics, regardless of the mean value of the local statistics.Therefore, as disclosed and claimed in copending U.S. Pat. No. ______entitled RADAR IMAGING SYSTEM AND METHOD USING SECOND MOMENT SPATIALVARIANCE, filed ______ by D. P. Bruyere et al. (Atty. Docket no. PD06W129), the second moment detector looks for a change in standarddeviation of a small, localized sampling of cells. This assumes that thetarget image has different second order statistics than the background,but places no constraint on the overall amplitude of the target withrespect to the background. Implied in this assumption is the fact thatthe size of the sample window needs to be smaller than the anticipatedsize of the target within the scene, but large enough to get a relativefeel for the local second order statistical properties. If the size ofthe sample area is too small, then the sampled statistics are notrepresentative of the actual second order properties associated with thearea under test.

However, if the size of the sample area is too large, then the samplemay be overlapping several parts of the scene with the resultant samplestatistics not representing any one part of the scene, but instead,combining sample statistics from different details within the scene. Itis for this reason that sufficient SAR resolution must be available tochoose a sample area large enough to get a reasonable feel for the localstatistics, but smaller than the smallest target size of interest.

FIG. 1 is a block diagram of an illustrative embodiment of an imagingradar system implemented in accordance with the present teachings. Asshown in FIG. 1, the system 10 includes a SAR antenna 12 coupled to acirculator 14. As is common in the art, the circulator 14 couples energyto the antenna 12 from a transmitter 16 in response to an exciter 18.The circulator 14 also couples energy from the antenna 12 to a receiver22 via a multiplexer 20. The receiver 22 down converts the received SARsignals and provides a baseband output to an analog to digital converter24. The A/D converter 24 outputs digital data to image processing,detection processing and track processing modules 26, 28 and 30respectively. In the best mode, the modules 26, 28 and 30 areimplemented in software. Transmit, receive and A/D timing and systemcontrol is provided by a conventional clock and control processor 40 inresponse to signals from a platform navigation and control system 50.The platform navigation and control system 50 also provides pointingangle control to the antenna 12 as is common in the art.

As discussed more fully below, the present invention is implementedwithin the detection-processing module 28 of FIG. 1. Detectionprocessing is illustrated in the flow diagram of FIG. 2.

FIG. 2 is a flow diagram of an illustrative embodiment of a method fordetection processing in accordance with the present teachings. Asillustrated in FIG. 2, the illustrative method 100 begins with aninitiation step 110 alter which at step 120 a detection Range/DopplerMatrix (RDM) is formed. At step 130 the RDM is thresholded and at step140 the thresholded RDMs are clustered. Finally, at step 150, thedetected spatial variances are output.

Gradient Magnitude Second Moment Detection

FIG. 3 is a flow diagram of an illustrative embodiment of a method forgradient magnitude second moment detection processing in accordance withthe teachings of the present invention. The method 120 includes aninitiation step 122 for each frame of radar image data. Next, at step124, a variance is calculated for each range-doppler matrix (RDM) pixelover an RDM matrix. The RDM matrix is a two dimensional m×n array ofreceived radar returns indexed by range in one dimension and Doppler inthe other dimension, where m and n are integers indicating the size of awindow used to calculate localized variance within a scene.

In accordance with the present teachings, at step 125, a two-dimensionalderivative of variance (i.e., the standard deviation in intensity) istaken to realize a more sensitive detector by looking for a high rate ofchange in variance. In the preferred embodiment, the technique used tocalculate the two dimensional derivative implements a Roberts method.See Image Processing, Analysis, and Machine Vision, by M. Sonka, V.Hlavac, and R. Boyle, PWS Publishing, (1999). Nonetheless, those ofordinary skill in the art will appreciate that other techniques forcalculating a high rate of change of variance may be used withoutdeparting from the scope of the present teachings.

To use the Roberts method of calculating the two-dimensional derivative,one calculates the intensity difference across the diagonals of fourimage pixels for all contiguous sets of four within the image, asillustrated in FIG. 4.

FIG. 4 is a diagram that illustrates the Roberts operation for taking atwo-dimensional derivative of variance in accordance with anillustrative embodiment of the present teachings. These intensitydifferences are normalized by a square root of two, to account for thefact that the difference is being taken across the diagonal, then thesquare root of the sum of the squares of the two diagonal derivativesprovides the gradient magnitude of the four pixel area centered in themiddle of the four pixel set. This is expressed as

$\begin{matrix}{{f_{1} = \frac{\left\lbrack {{f\left( {r,c} \right)} - {f\left( {{r - 1},{c - 1}} \right)}} \right\rbrack}{\sqrt{2}}}{f_{2} = \frac{\left\lbrack {{f\left( {{r - 1},c} \right)} - {f\left( {r,{c - 1}} \right)}} \right\rbrack}{\sqrt{2}}}{{{\Delta \overset{\_}{f}}} = \sqrt{f_{1}^{2} + f_{2}^{2}}}} & (0.12)\end{matrix}$

where |Δ f| is the gradient magnitude and f₁ and f₂ are the intermediatediagonal derivatives. The advantage of the Roberts derivative operatoris the fact that only four pixel elements are required and thecalculated gradient is centered in the middle of the four pixels used inthe calculation.

The reason that we chose to analyze the gradient magnitude of the secondmoment image is that it should have some advantages over the secondmoment image itself. Some naturally occurring image phenomenology existsthat might trigger an absolute measure of variance, such as theintensity of the antenna beam pattern reflecting off of a field ofgrass. The variance in the center of the beam would be higher than thesides of the beam, yet we would not want to consider the center of thebeam pattern in a uniform field of grass as a legitimate thresholdcrossing. Since the rate of change of increased variance associated withthe beam pattern intensity would be slower than the rate of change ofvariance from man made target, then this may prove to be a betterdetector under certain circumstances. This should reduce the number offalse alarms due to beam pattern roll off, or other naturally occurringphenomena such as reflectivity changes associated with grassy fields.

The invention capitalizes on the fact that target returns second orderstatistics change faster than second order statistic of backgroundclutter due to rapid changes in target reflectivity.

FIG. 5 is a flow diagram in more detail of an illustrative embodiment ofa method for gradient magnitude second moment detection processing inaccordance with the teachings of the present invention. As shown in FIG.5, each input image 130 is comprised of a plurality of pixel elements128, each of which represents variance of scene amplitude cross rangeand down range. At step 132 the two dimensional first derivative istaken. At step 134, an output variance derivative image is created withrespect to the variance (σ²) in the cross range and down rangedirections. Each element 136 in the output variance derivative image 134represents a rate of change of variance at the designated cross rangeand down range coordinates. Each element 136 in the derivative image 134is then compared to a threshold at step 130 to provide an outputdetection signal.

Returning to FIG. 3, at step 130, detection thresholding is performed onthe variance/RDM. At step 130, the algorithm outputs a set oftwo-dimensional vectors pointing to those RDM locations that had a rateof change of variance larger than the predetermined threshold.

Thus, the present invention has been described herein with reference toa particular embodiment for a particular application. Those havingordinary skill in the art and access to the present teachings willrecognize additional modifications applications and embodiments withinthe scope thereof.

It is therefore intended by the appended claims to cover any and allsuch applications, modifications and embodiments within the scope of thepresent invention.

Accordingly,

1. A detection system comprising: means for receiving a frame of imagedata; means for performing a rate of change of variance calculation withrespect to at least one pixel in said frame of image data; and means forcomparing said calculated rate of change of variance with apredetermined threshold to provide output data.
 2. The invention ofclaim 1 wherein said frame of image data includes a range/Dopplermatrix.
 3. The invention of claim 2 wherein said range/Doppler matrixincludes N down range samples and M cross range samples.
 4. Theinvention of claim 2 wherein said means for performing a rate of changeof variance calculation includes means for calculating a rate of changeof variance over an N×M window within said range/Doppler matrix.
 5. Theinvention of claim 4 wherein said means for performing a rate of changeof variance calculation outputs a rate of change of variance pixel map.6. The invention of claim 1 wherein said means for performing a rate ofchange of variance calculation includes means for identifying a changein a standard deviation of a small, localized sampling of cells.
 7. Aradar system comprising: a radar antenna; a transmitter; a receiver;circulator means for coupling said transmitter and receiver to saidantenna; an image processor coupled to said receiver; and a detectionprocessor coupled to said image processor, said detection processorhaving: software for receiving a frame of image data; software forperforming a rate of change of variance calculation with respect to atleast one pixel in said frame of image data; and software for comparingsaid calculated rate of change of variance with a predeterminedthreshold to provide output data.
 8. The invention of claim 7 whereinsaid frame of image data includes a range/Doppler matrix.
 9. Theinvention of claim 8 wherein said range/Doppler matrix includes N downrange samples and M cross range samples.
 10. The invention of claim 8wherein said software for performing a rate of change of variancecalculation includes software for calculating a rate of change ofvariance over an N×M window within said range/Doppler matrix.
 11. Theinvention of claim 10 wherein said software for performing a rate ofchange of variance calculation outputs a rate of change of variancepixel map.
 12. The invention of claim 7 wherein said software forperforming a rate of change of variance calculation includes softwarefor identifying a change in a standard deviation of a small, localizedsampling of cells.
 13. The invention of claim 7 further including atrack processor.
 14. A detection method comprising the steps of:receiving a frame of image data; performing a rate of change of variancecalculation with respect to at least one pixel in said frame of imagedata; and comparing said calculated rate of change of variance with apredetermined threshold to provide output data.